Constructing a constitutive model of knitted fabric

Knitting is an ancient technology wherein yarn is manipulated into an array of slipknots to form fabric. By patterning these stitches in different ways, one can create fabrics possessing a wide array of elasticities and geometries, without needing to change the type of yarn being used. Thus, knitting is a way of programming material properties via a code that describes stitch patterns. However, while there have been mechanical models of aspects of knitted fabric, there is currently no unifying description that models knitted fabric elasticity given a prescribed stitch pattern. To make progress towards this end, we seek a method of generating constitutive relations for a given stitch pattern. Using a geometric framework in which yarn degrees of freedom are modeled as elastic space curves, with stitches held together by contact interactions, we solve for energy-minimizing stitch structures numerically within the unit cell of a given pattern. We then extract the constitutive relations by monitoring the deformation of the stitch given external stresses on the unit cell. This method not only gives us predicted stress-versus-strain relations that compare favorably with experiments but it allows us to probe the role of yarn geometry in determining fabric mechanics.